Our bunny Gandy does the same thing!! We have those cubes for his cage also (but ours are covered in that white plastic stuff) and he chews on them all the time. He actually chewed so hard that he managed to pull one of the metal bars away – I know, insane, right!!!!
I am pretty sure his issue is wanting to be outside though, because we have one cube bit that we flip open as the door in and out, and he chews on that one all the time when we are in the house and he is shut inside. But now he has also started chewing on one that is on the side as well.
We cover his house over with a sheet during the day when we are at work (so he wont set the security alarm off!) and at night, and we have noticed that when he starts chewing, if we out the sheet down in front of where he is chewing he will stop.
And I have actually noticed that he has stopped chewing as much the last week or so. So hopefully he is getting over it now
We thought perhaps his initial issue was that, he used to be kept in an outdoor hutch (we rent and only just got permission to be “allowed” to keep him inside) so when he used to come inside when we were home, he was allowed to go where ever he wanted. Now that he lives inside, he sometimes has to be shut away – but he was so used to inside = freedom, that he didnt like being inside and still shut up.